BACHELOR OF BUSINESS ADMINISTRATION

BUSINESS ADMINISTRATION

BUSINESS ECONOMICS

Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
For a skewed distribution, what is the minimum percentage of the observations that will lie within 2.5 standard deviations of the mean based on Chebyshev’s rule?
A
84%
B
75%
C
78%
D
95%
Explanation: 

Detailed explanation-1: -So you can substitute the value of k into the equation and determine the minimum percentage, so you have 1 minus 1 over k, which is 2.5 squared, so this becomes 1 minus 1. Over 2.5 square is 6.25. We have 1 minus 0.16 and this is equal to 0.84 in this comb translated as 84 percent.

Detailed explanation-2: -Therefore, 98.76% of the area of standard normal distribution is within 2.5 standard deviation of the mean.

Detailed explanation-3: -Approximately 95% of the data fall within two standard deviations of the mean. Approximately 99.7% of the data fall within three standard deviations of the mean.

Detailed explanation-4: -Consequently, Chebyshev’s Theorem tells you that at least 75% of the values fall between 100 ± 20, equating to a range of 80 – 120. Conversely, no more than 25% fall outside that range.

Detailed explanation-5: -For a skewed distribution that has excess kurtosis, the minimum percentage of the distribution within three standard deviations of the mean is closest to: A 89%.

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